Abstract

We demonstrated a beam conformal projection system for coherent combining of large-scale lasers over 2.1 km in turbulence 20 m above the ground, using the basic modules of a 19-element fiber phased array combined with coarse pointing by a gimbal mount. After coarse pointing and aberration corrections, the metrics (reflected light) of the combined beams from a basic module were best increased by 13.4 times, suggesting that our system promises the great effect of coherent combining under long-distance turbulence. Moreover, we tentatively realized coherent combining of two basic modules (38 lasers), which is the largest number of elements in a fiber laser coherent beam combination outdoors, to the best of our knowledge, with the metrics of combined beams increased by about 29 times.

© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement

Actively coherent beam combining (CBC) has been proven to be a promising method to obtain high brightness laser outputs, which is important for such applications as laser communications, lidar, energy delivery, etc. [113]. Currently, most experiments have been conducted indoors, where the maximum combined power is over 10 kW with a maximum of over 100 elements of the beamlets [9,10]. These reports demonstrated the great potential of CBC to break the power limitation of a single fiber laser [1420], but few of them can be applied to energy delivery over long distances because of aberrations induced by atmospheric turbulence during transmission. Target-in-the-loop (TIL) introduced to the CBC system is expected to effectively eliminate these influences to improve the brightness of the combined beam. However, current TIL research mainly focuses on simulation and lacks corresponding experiments. Furthermore, parallel projection was adopted in most CBC experiments, but this method is not suitable for short-range applications where the propagation distance is less than the Rayleigh distance of the equivalent large aperture beam. The beamlets will not overlap entirely; thus, the brightness of the combined beam would be decreased [3,6]. This effect would be increased for larger numbers of the array’s sub-apertures for future applications. Theoretical research has shown that the conformal projection method based on an adaptive fiber optics collimator (AFOC) array through TIL can solve this problem over several kilometers (near-field) [5,7]. By controlling the piston phase and the tip/tilt phase of the beamlets, the wavefront distribution will be close to the shape of a focused spherical wave so that a combined beam with a higher brightness than the parallel projection can be obtained [21,22]. Up to now, there have rarely been experimental reports on the conformal projection of the CBC system in a turbulent environment. In 2011 and 2016, Weyrauch et al. [1,2] used the conformal projection method with piston phase controlling to compensate for real atmospheric turbulence using the delayed stochastic parallel gradient descent (SPGD) algorithm. In 2021, Rouzé et al. [4] reported high-speed and high-precision piston aberration compensation of a seven-element CBC system using a single-detector electronic-frequency tagging technique. However, these reports have not shown the improved effect of tip/tilt aberration compensation. In this Letter, numerical simulation of the influence of parallel projection and conformal projection method on the brightness of the combined beam is given first, where the advantage of the conformal projection method in the near-field CBC applications is proven. We verified this method in the CBC experiment of 19 laser beams over 2.1 km in real turbulence. The metric (reflected light) of the combined beam has been significantly increased after using the conformal projection and correcting piston aberrations and tip/tilt aberrations. Finally, we tentatively realized the coherent combining of 38 laser beams using two 19-element CBC modules based on this method, which reveals the potential of expanding to arrays with hundreds of sub-apertures.

The simulation model of TIL CBC is established according to the parameters of the 19-element CBC system that we previously reported [15,16]. The hexagonal array’s whole aperture size D is 152 mm, which allows for the angular diameter of the power in the bucket (PIB) to be 2.44λ/D (Airy disk diameter, 17.08 µrad) and the sub-aperture size d is 28 mm. The influence of the beamlet propagation method on coherent combining in different transmission distances is analyzed here. For simplicity, the impact of atmospheric turbulence is ignored. The characteristics of the combined beams from the Rayleigh distance of the beamlet (0.25πd2/λ, 578 m, wavelength λ of 1064 nm) to the Rayleigh distance of equivalent aperture (0.25πD2/λ, 17.05 km) are given in Fig. 1. As shown in Figs. 1(a)–1(d), we proposed four methods to project the beamlets by adjusting the corresponding piston and tip/tilt phases. The methods include parallel projection (PP), conformal projection by piston control (CPPC), conformal projection by piston and tip/tilt control (CPPTC), and ideal projection (IP). The wavefront distribution shown in Fig. 1(c) is closer to a convergent spherical wave, shown in Fig. 1(d). From Fig. 1(e), we learn that a superior coherent combining can be achieved within 5 km via CPPTC. Figure 2 shows the patterns of the combined beams with a transmission distance of 2.1 km. As shown in Fig. 2(a), the PIB by the PP method is 0.0377, with a weak light intensity distribution. However, as shown in Figs. 2(b)–2(d), the PIB is 0.3125, 0.4988, and 0.5147 by CPPC, CPPTC, and, IP respectively. It can be seen that the CPPTC method allows a better PIB. Furthermore, the Rayleigh distance (far-field) is directly proportional to D2. Thus, applying the CPPTC method for future large-scale TIL CBC systems in near-field applications is necessary, especially over several kilometers.

 figure: Fig. 1.

Fig. 1. (a)–(d) Schematic diagram of different beamlet propagation methods. (e) Corresponding PIB for different transmission distances.

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 figure: Fig. 2.

Fig. 2. Corresponding patterns of different propagation methods.

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The experimental setting is illustrated schematically in Fig. 3. The seed laser is amplified to 250 mW and then divided into 19 beamlets. All the beamlets go through piezoelectric phase compensators (PCs) to correct the piston aberration and are then connected to the AFOCs, which control the beam direction to precisely track the target and correct the tip/tilt aberration. The PC has a half-wave voltage of approximately 2.5 V and a first-order resonance frequency of approximately 32 kHz. The AFOC has a deflection angle range of ±0.2 mrad and a first-order resonance frequency of about 2 kHz. The control signal is amplified 100 times by a high-voltage amplifier (HVA). The distance between adjacent beamlets is s = 31 mm, allowing a filling factor (d/s) of 0.903. At the beginning, the collimated beamlets propagate to the target in the form of PP in a turbulent environment with a path of 2.1 km (20 m above ground). An aluminum plate with a hole (Φ = 50 mm) in the center is placed at a target screen to observe the CBC pattern using a charge coupled device (CCD) camera. A corner reflector (CR) is placed at the back of the hole to reflect the combined beam. The hole is covered with an annular plate (inner diameter, 30 mm; outer diameter, 50 mm), to adjust the reflecting area, and a small disk (diameter, 10 mm), to observe changes of the peak power, which is positively correlated with the Strehl ratio. An annular optical diaphragm with an inner diameter of 10 mm and an outer diameter of 30 mm is then formed. The back-reflected light passing through the diaphragm and the atmosphere path is received by a local telescope and detected by a photodetector (PD) as a voltage (metric J), which is positively correlated with the PIB value defined previously. The controller precisely corrects the piston aberration and tip/tilt aberration using the SPGD algorithm. Eight LED beads producing distinct contours are set on the edge of the screen, for the pointing of the gimbal mount (GM). A differential image motion monitor (DIMM) is employed to measure the Fried coherence length (r0). The method involves measuring wavefront slope differences over two small pupils some distance apart [23]. In this experiment, the iteration rates of the SPGD algorithm are about 10 kHz for correcting piston aberration and 1 kHz for correcting tip/tilt aberration [15,16].

 figure: Fig. 3.

Fig. 3. Experimental setup and principle of pointing and coherent combining 19 lasers over 2.1 km in turbulence.

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Before coherent combining, we should employ the GM to coarsely point to the CR so that adequate optical signals return to the controller. An image containing light intensity, where intensity less than that of the LED beads will be treated as zero, was calculated by the centroid algorithm to obtain the miss distance. In this way, the CR is lighted, and the telescope receives enough reflected light when the GM aims the target. As shown in Fig. 4, we have corrected the miss distance of about 6 mrad in the “GM on” state. Compared with the “GM off” state, the telescope can successfully observe the light returned from the CR.

 figure: Fig. 4.

Fig. 4. Image of target screen captured by telescope: (a) GM off; (b) GM on.

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On a cloudy day (June 27, 2021), a series of experimental results of CBC by SPGD under different turbulence intensities (characterized by D/r0) after the system shifted into the “GM on” state were collected. The average maximum and minimum local temperatures were 32°C and 25°C, with a wind speed on the Beaufort scale of 3 and 85% air humidity. To evaluate the improvement effect of coherent combining, we collect corresponding metrics J in Fig. 5 at different stages during the experiment, for open loop (OP), phase locking (PL), and phase locking plus tip/tilt correction (PLTT). The normalized average metrics of J are listed in Table 1. In general, a higher value of J means a better PIB, and the effect of coherent combining will deteriorate with increasing turbulence. Compared with the OP, the average metrics of PL were increased by 9.3, 7.6, and 1.6 times for D/r0 of 1.588, 2.634, and 4.221, respectively, while the average metrics of PLTT were increased by 13.4, 9.1, and 3.9 times, respectively, under the corresponding D/r0. The effects were improved greatly after PLTT in different levels of turbulence; especially at D/r0=4.221, metrics could not converge to an acceptable value until the tip/tilt was corrected and the average metrics of PLTT were increased about 2.4 times compared with PL. These experiments indicate that the purely PL control cannot obtain a better combining effect even in weak turbulence. It should be noted that PL (or PLTT) here is equivalent to the CPPC (or CPPTC) defined previously. The increment of the metric J from PL to PLTT under weak turbulence (D/r0=1.588) is about 1.44 times, which is close to the 1.59 times ideal PIB, increasing from CPPC to CPPTC.

 figure: Fig. 5.

Fig. 5. Metrics of combined beams at different stages.

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Tables Icon

Table 1. Normalized Average Metrics at Different Stages in Different Turbulence

Figure 6 shows 30 s exposure images through multi-frame superposition on the target screen for each state. The white lines present the intensity value curve along the horizontal axis in the center. Considering the speckle effect caused by the rough aluminum plate, the far-field patterns on the aluminum screen are processed by mean filtering. The maximum values of the figures are unified for each turbulence intensity. At the OP state, there is nearly no interference pattern at the target surface in Figs. 6(a), 6(d), and 6(g). The projection method and the aberrations induced by turbulence limit the combining effect, so the peak power is weak. Some lobes of the coherent combining appear in Figs. 6(b), 6(e), and 6(h), where the peak powers are 2.58, 2.43, and 1.51 times higher than the OP state, respectively. This means that, after the PL control, this projection method could improve a part of the combining effect and compensate for piston aberrations induced by turbulence, especially in weak turbulence. At the PLTT state, clear interference patterns can be observed with six side lobes in Figs. 6(c), 6(f), and 6(i), and the peak powers are 7.45, 5.19, and 3.13 times higher than the OP state, respectively, reaching the highest level.

 figure: Fig. 6.

Fig. 6. Patterns of combined beams at different stages.

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To illustrate the scalability of the array, we extend the number of AFOCs to 57 by using three 19-element CBC modules, where 38 of them are employed for TIL CBC demonstration and the total emissive power is equal to the power of the 19-element CBC system (250 mW), as shown in Fig. 7(a). We obtained the metric and far-field long exposure images of the 38-element CBC system using the same control strategy, D/r0=1.835. As shown in Figs. 7(c)–7(f), when the system enters the PLTT state, the metric has increased by about 29 times. The interference pattern is clearer than the OP state and similar to the ideal pattern shown in Fig. 7(b). The ratio of the peak intensity of the 38-element CBC system to that of the 19-element system is 1.57, as shown in Fig. 6(c) and Fig. 7(c), where the theoretical ratio is 2. This result indicates that the brightness can be improved when the number of laser beams is scaled to 38. However, the results of PLTT correction shown in Fig. 6(c) and Fig. 7(e) are still poorer than the ideal correction. This phenomenon is partly caused by high-frequency dynamic atmospheric turbulence and the low iteration rate of the PC controller. Also, the method of PLTT has a physical limitation that cannot completely compensate for the turbulence [21,22]. Therefore, we could employ high-speed field programmable gate array (FPGA) processors to achieve a higher iteration rate and adopt amplitude and phase (piston + tip/tilt) control to achieve better effects in the future.

 figure: Fig. 7.

Fig. 7. (a) Emissive plane of 38-element CBC system. (b) Ideal pattern of combined beam. (c)–(e) Patterns of combined beams at OP, PL, and PLTT stages, respectively. (f) Average metric of the combined beam.

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In conclusion, we theoretically and experimentally testified the superiority of the coherent conformal projection system. We demonstrate the large-angle pointing control and coherent combining of 19 laser beams with a nearly horizontal transmission angle over 2.1 km in turbulence 20 m above the ground, using TIL CBC technology combined with coarse pointing by a GM. The result shows an excellent effect of coherent combining in different levels of turbulence. These results promise that our system can be conveniently used in outdoor practical applications with a transmission distance of several kilometers. By taking the 19-element TIL CBC system as a basic module, we also realized the coherent combining of 38 laser beams to generate a brighter combined beam, indicating the scalability of array lasers. We intend to conduct TIL CBC experiments on larger-scale arrays in the future.

Funding

National Natural Science Foundation of China (62005286, 62175241).

Disclosures

The authors declare no conflicts of interest.

Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

REFERENCES

1. T. Weyrauch, M. Vorontsov, G. Carhar, L. Beresnev, A. Rostov, E. E. Polnau, and J. J. Liu, Opt. Lett. 36, 4455 (2011). [CrossRef]  

2. T. Weyrauch, M. Vorontsov, J. Angano, V. Ovchinnikov, D. Bricker, E. Polnau, and A. Rostov, Opt. Lett. 41, 840 (2016). [CrossRef]  

3. M. A. Vorontsov and T. Weyrauch, Appl. Opt. 55, 9950 (2016). [CrossRef]  

4. B. Rouzé, L. Lombard, H. Jacqmin, A. Liméry, A. Durécu, and P. Bourdon, Appl. Opt. 60, 8524 (2021). [CrossRef]  

5. G Huang, G Lv, Y Fan, C Geng, and X. Li, Opt. Lasers Eng. 148, 106753 (2022). [CrossRef]  

6. D. Zhi, Y. Ma, R. Tao, P. Zhou, X. Wang, Z. Chen, and L. Si, Sci. Rep. 9, 2783 (2019). [CrossRef]  

7. M. Vorontsov, G. Filimonov, V. Vchinnikov, E. Polnau, S. Lachinova, T. Weyrauch, and J. Mangano, Appl. Opt. 55, 4170 (2016). [CrossRef]  

8. Y. Zheng, Y. Yang, J. Wang, M. Hu, G. Liu, X. Zhao, X. Chen, K. Liu, C. Zhao, B. He, and J. Zhou, Opt. Express 24, 12063 (2016). [CrossRef]  

9. E. Shekel, Y. Vidne, and B. Urbach, Proc. SPIE 11260, 1126021 (2020). [CrossRef]  

10. H. Chang, Q. Chang, J. Xi, T. Hou, R. Su, P. Ma, J. Wu, C. Li, M. Jiang, Y. Ma, and P. Zhou, Photonics Res. 8, 1943 (2020). [CrossRef]  

11. M. Vorontsov and V. Sivokon, J. Opt. Soc. Am. A 15, 2745 (1998). [CrossRef]  

12. M. Björck, M. Henriksson, and L. Sjöqvist, Proc. SPIE 11867, 118670E (2021). [CrossRef]  

13. G. Huang, C. Geng, F. Li, Y. Yang, and X. Li, IEEE Photonics J. 10, 7904212 (2018). [CrossRef]  

14. M. Björck, M. Henriksson, and L. Sjökvist, Appl. Opt. 60, 4366 (2021). [CrossRef]  

15. J. Zuo, F. Li, C. Geng, F. Zou, J. Jiang, J. Liu, X. Yang, T. Yu, G. Huang, Z. Fan, B. Li, and X. Li, IEEE Photonics J. 13, 1500113 (2021). [CrossRef]  

16. C. Geng, F. Li, J. Zuo, J. Liu, X. Yang, T. Yu, J. Jiang, and X. Li, Opt. Lett. 45, 1906 (2020). [CrossRef]  

17. M. Oermann, N. Carmody, A. Hemming, S. Rees, N. Simakov, R. Swain, K. Boyd, A. Davidson, L. Corena, D. Stepanov, and J. Haub, Opt. Express 26, 6715 (2018). [CrossRef]  

18. D. Wang, Q. Du, T. Zhou, D. Li, and R. Wilcox, Opt. Express 29, 5694 (2021). [CrossRef]  

19. A. Boju, G. Maulion, J. Saucourt, J. Levalj, J. Ledortz, A. Koudoro, J. Berthomier, M. Naiim-Habib, P. Armand, V. Kermene, A. Desfarges-Berthelemot, and A. Barthelemy, Opt. Express 29, 11445 (2021). [CrossRef]  

20. H. Tünnermann and A. Shirakawa, Opt. Express 27, 24223 (2019). [CrossRef]  

21. K. F. Yu, O. L. Antipov, N. A. Makenova, and V. P. Lukin, Proc. SPIE 9680, 96801D (2015). [CrossRef]  

22. O. L. Antipov, K. F. Yu, V. P. Lukin, and N. A. Makenova, Proc. SPIE 10035, 100351R (2016). [CrossRef]  

23. M. Sarazin and F. Roddier, Astron. Astrophys. 227, 294 (1990).

References

  • View by:

  1. T. Weyrauch, M. Vorontsov, G. Carhar, L. Beresnev, A. Rostov, E. E. Polnau, and J. J. Liu, Opt. Lett. 36, 4455 (2011).
    [Crossref]
  2. T. Weyrauch, M. Vorontsov, J. Angano, V. Ovchinnikov, D. Bricker, E. Polnau, and A. Rostov, Opt. Lett. 41, 840 (2016).
    [Crossref]
  3. M. A. Vorontsov and T. Weyrauch, Appl. Opt. 55, 9950 (2016).
    [Crossref]
  4. B. Rouzé, L. Lombard, H. Jacqmin, A. Liméry, A. Durécu, and P. Bourdon, Appl. Opt. 60, 8524 (2021).
    [Crossref]
  5. G Huang, G Lv, Y Fan, C Geng, and X. Li, Opt. Lasers Eng. 148, 106753 (2022).
    [Crossref]
  6. D. Zhi, Y. Ma, R. Tao, P. Zhou, X. Wang, Z. Chen, and L. Si, Sci. Rep. 9, 2783 (2019).
    [Crossref]
  7. M. Vorontsov, G. Filimonov, V. Vchinnikov, E. Polnau, S. Lachinova, T. Weyrauch, and J. Mangano, Appl. Opt. 55, 4170 (2016).
    [Crossref]
  8. Y. Zheng, Y. Yang, J. Wang, M. Hu, G. Liu, X. Zhao, X. Chen, K. Liu, C. Zhao, B. He, and J. Zhou, Opt. Express 24, 12063 (2016).
    [Crossref]
  9. E. Shekel, Y. Vidne, and B. Urbach, Proc. SPIE 11260, 1126021 (2020).
    [Crossref]
  10. H. Chang, Q. Chang, J. Xi, T. Hou, R. Su, P. Ma, J. Wu, C. Li, M. Jiang, Y. Ma, and P. Zhou, Photonics Res. 8, 1943 (2020).
    [Crossref]
  11. M. Vorontsov and V. Sivokon, J. Opt. Soc. Am. A 15, 2745 (1998).
    [Crossref]
  12. M. Björck, M. Henriksson, and L. Sjöqvist, Proc. SPIE 11867, 118670E (2021).
    [Crossref]
  13. G. Huang, C. Geng, F. Li, Y. Yang, and X. Li, IEEE Photonics J. 10, 7904212 (2018).
    [Crossref]
  14. M. Björck, M. Henriksson, and L. Sjökvist, Appl. Opt. 60, 4366 (2021).
    [Crossref]
  15. J. Zuo, F. Li, C. Geng, F. Zou, J. Jiang, J. Liu, X. Yang, T. Yu, G. Huang, Z. Fan, B. Li, and X. Li, IEEE Photonics J. 13, 1500113 (2021).
    [Crossref]
  16. C. Geng, F. Li, J. Zuo, J. Liu, X. Yang, T. Yu, J. Jiang, and X. Li, Opt. Lett. 45, 1906 (2020).
    [Crossref]
  17. M. Oermann, N. Carmody, A. Hemming, S. Rees, N. Simakov, R. Swain, K. Boyd, A. Davidson, L. Corena, D. Stepanov, and J. Haub, Opt. Express 26, 6715 (2018).
    [Crossref]
  18. D. Wang, Q. Du, T. Zhou, D. Li, and R. Wilcox, Opt. Express 29, 5694 (2021).
    [Crossref]
  19. A. Boju, G. Maulion, J. Saucourt, J. Levalj, J. Ledortz, A. Koudoro, J. Berthomier, M. Naiim-Habib, P. Armand, V. Kermene, A. Desfarges-Berthelemot, and A. Barthelemy, Opt. Express 29, 11445 (2021).
    [Crossref]
  20. H. Tünnermann and A. Shirakawa, Opt. Express 27, 24223 (2019).
    [Crossref]
  21. K. F. Yu, O. L. Antipov, N. A. Makenova, and V. P. Lukin, Proc. SPIE 9680, 96801D (2015).
    [Crossref]
  22. O. L. Antipov, K. F. Yu, V. P. Lukin, and N. A. Makenova, Proc. SPIE 10035, 100351R (2016).
    [Crossref]
  23. M. Sarazin and F. Roddier, Astron. Astrophys. 227, 294 (1990).

2022 (1)

G Huang, G Lv, Y Fan, C Geng, and X. Li, Opt. Lasers Eng. 148, 106753 (2022).
[Crossref]

2021 (6)

2020 (3)

C. Geng, F. Li, J. Zuo, J. Liu, X. Yang, T. Yu, J. Jiang, and X. Li, Opt. Lett. 45, 1906 (2020).
[Crossref]

E. Shekel, Y. Vidne, and B. Urbach, Proc. SPIE 11260, 1126021 (2020).
[Crossref]

H. Chang, Q. Chang, J. Xi, T. Hou, R. Su, P. Ma, J. Wu, C. Li, M. Jiang, Y. Ma, and P. Zhou, Photonics Res. 8, 1943 (2020).
[Crossref]

2019 (2)

D. Zhi, Y. Ma, R. Tao, P. Zhou, X. Wang, Z. Chen, and L. Si, Sci. Rep. 9, 2783 (2019).
[Crossref]

H. Tünnermann and A. Shirakawa, Opt. Express 27, 24223 (2019).
[Crossref]

2018 (2)

2016 (5)

2015 (1)

K. F. Yu, O. L. Antipov, N. A. Makenova, and V. P. Lukin, Proc. SPIE 9680, 96801D (2015).
[Crossref]

2011 (1)

1998 (1)

1990 (1)

M. Sarazin and F. Roddier, Astron. Astrophys. 227, 294 (1990).

Angano, J.

Antipov, O. L.

O. L. Antipov, K. F. Yu, V. P. Lukin, and N. A. Makenova, Proc. SPIE 10035, 100351R (2016).
[Crossref]

K. F. Yu, O. L. Antipov, N. A. Makenova, and V. P. Lukin, Proc. SPIE 9680, 96801D (2015).
[Crossref]

Armand, P.

Barthelemy, A.

Beresnev, L.

Berthomier, J.

Björck, M.

M. Björck, M. Henriksson, and L. Sjökvist, Appl. Opt. 60, 4366 (2021).
[Crossref]

M. Björck, M. Henriksson, and L. Sjöqvist, Proc. SPIE 11867, 118670E (2021).
[Crossref]

Boju, A.

Bourdon, P.

Boyd, K.

Bricker, D.

Carhar, G.

Carmody, N.

Chang, H.

H. Chang, Q. Chang, J. Xi, T. Hou, R. Su, P. Ma, J. Wu, C. Li, M. Jiang, Y. Ma, and P. Zhou, Photonics Res. 8, 1943 (2020).
[Crossref]

Chang, Q.

H. Chang, Q. Chang, J. Xi, T. Hou, R. Su, P. Ma, J. Wu, C. Li, M. Jiang, Y. Ma, and P. Zhou, Photonics Res. 8, 1943 (2020).
[Crossref]

Chen, X.

Chen, Z.

D. Zhi, Y. Ma, R. Tao, P. Zhou, X. Wang, Z. Chen, and L. Si, Sci. Rep. 9, 2783 (2019).
[Crossref]

Corena, L.

Davidson, A.

Desfarges-Berthelemot, A.

Du, Q.

Durécu, A.

Fan, Y

G Huang, G Lv, Y Fan, C Geng, and X. Li, Opt. Lasers Eng. 148, 106753 (2022).
[Crossref]

Fan, Z.

J. Zuo, F. Li, C. Geng, F. Zou, J. Jiang, J. Liu, X. Yang, T. Yu, G. Huang, Z. Fan, B. Li, and X. Li, IEEE Photonics J. 13, 1500113 (2021).
[Crossref]

Filimonov, G.

Geng, C

G Huang, G Lv, Y Fan, C Geng, and X. Li, Opt. Lasers Eng. 148, 106753 (2022).
[Crossref]

Geng, C.

J. Zuo, F. Li, C. Geng, F. Zou, J. Jiang, J. Liu, X. Yang, T. Yu, G. Huang, Z. Fan, B. Li, and X. Li, IEEE Photonics J. 13, 1500113 (2021).
[Crossref]

C. Geng, F. Li, J. Zuo, J. Liu, X. Yang, T. Yu, J. Jiang, and X. Li, Opt. Lett. 45, 1906 (2020).
[Crossref]

G. Huang, C. Geng, F. Li, Y. Yang, and X. Li, IEEE Photonics J. 10, 7904212 (2018).
[Crossref]

Haub, J.

He, B.

Hemming, A.

Henriksson, M.

M. Björck, M. Henriksson, and L. Sjökvist, Appl. Opt. 60, 4366 (2021).
[Crossref]

M. Björck, M. Henriksson, and L. Sjöqvist, Proc. SPIE 11867, 118670E (2021).
[Crossref]

Hou, T.

H. Chang, Q. Chang, J. Xi, T. Hou, R. Su, P. Ma, J. Wu, C. Li, M. Jiang, Y. Ma, and P. Zhou, Photonics Res. 8, 1943 (2020).
[Crossref]

Hu, M.

Huang, G

G Huang, G Lv, Y Fan, C Geng, and X. Li, Opt. Lasers Eng. 148, 106753 (2022).
[Crossref]

Huang, G.

J. Zuo, F. Li, C. Geng, F. Zou, J. Jiang, J. Liu, X. Yang, T. Yu, G. Huang, Z. Fan, B. Li, and X. Li, IEEE Photonics J. 13, 1500113 (2021).
[Crossref]

G. Huang, C. Geng, F. Li, Y. Yang, and X. Li, IEEE Photonics J. 10, 7904212 (2018).
[Crossref]

Jacqmin, H.

Jiang, J.

J. Zuo, F. Li, C. Geng, F. Zou, J. Jiang, J. Liu, X. Yang, T. Yu, G. Huang, Z. Fan, B. Li, and X. Li, IEEE Photonics J. 13, 1500113 (2021).
[Crossref]

C. Geng, F. Li, J. Zuo, J. Liu, X. Yang, T. Yu, J. Jiang, and X. Li, Opt. Lett. 45, 1906 (2020).
[Crossref]

Jiang, M.

H. Chang, Q. Chang, J. Xi, T. Hou, R. Su, P. Ma, J. Wu, C. Li, M. Jiang, Y. Ma, and P. Zhou, Photonics Res. 8, 1943 (2020).
[Crossref]

Kermene, V.

Koudoro, A.

Lachinova, S.

Ledortz, J.

Levalj, J.

Li, B.

J. Zuo, F. Li, C. Geng, F. Zou, J. Jiang, J. Liu, X. Yang, T. Yu, G. Huang, Z. Fan, B. Li, and X. Li, IEEE Photonics J. 13, 1500113 (2021).
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Appl. Opt. (4)

Astron. Astrophys. (1)

M. Sarazin and F. Roddier, Astron. Astrophys. 227, 294 (1990).

IEEE Photonics J. (2)

J. Zuo, F. Li, C. Geng, F. Zou, J. Jiang, J. Liu, X. Yang, T. Yu, G. Huang, Z. Fan, B. Li, and X. Li, IEEE Photonics J. 13, 1500113 (2021).
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G. Huang, C. Geng, F. Li, Y. Yang, and X. Li, IEEE Photonics J. 10, 7904212 (2018).
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J. Opt. Soc. Am. A (1)

Opt. Express (5)

Opt. Lasers Eng. (1)

G Huang, G Lv, Y Fan, C Geng, and X. Li, Opt. Lasers Eng. 148, 106753 (2022).
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Opt. Lett. (3)

Photonics Res. (1)

H. Chang, Q. Chang, J. Xi, T. Hou, R. Su, P. Ma, J. Wu, C. Li, M. Jiang, Y. Ma, and P. Zhou, Photonics Res. 8, 1943 (2020).
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Proc. SPIE (4)

M. Björck, M. Henriksson, and L. Sjöqvist, Proc. SPIE 11867, 118670E (2021).
[Crossref]

K. F. Yu, O. L. Antipov, N. A. Makenova, and V. P. Lukin, Proc. SPIE 9680, 96801D (2015).
[Crossref]

O. L. Antipov, K. F. Yu, V. P. Lukin, and N. A. Makenova, Proc. SPIE 10035, 100351R (2016).
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E. Shekel, Y. Vidne, and B. Urbach, Proc. SPIE 11260, 1126021 (2020).
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Sci. Rep. (1)

D. Zhi, Y. Ma, R. Tao, P. Zhou, X. Wang, Z. Chen, and L. Si, Sci. Rep. 9, 2783 (2019).
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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Figures (7)

Fig. 1.
Fig. 1. (a)–(d) Schematic diagram of different beamlet propagation methods. (e) Corresponding PIB for different transmission distances.
Fig. 2.
Fig. 2. Corresponding patterns of different propagation methods.
Fig. 3.
Fig. 3. Experimental setup and principle of pointing and coherent combining 19 lasers over 2.1 km in turbulence.
Fig. 4.
Fig. 4. Image of target screen captured by telescope: (a) GM off; (b) GM on.
Fig. 5.
Fig. 5. Metrics of combined beams at different stages.
Fig. 6.
Fig. 6. Patterns of combined beams at different stages.
Fig. 7.
Fig. 7. (a) Emissive plane of 38-element CBC system. (b) Ideal pattern of combined beam. (c)–(e) Patterns of combined beams at OP, PL, and PLTT stages, respectively. (f) Average metric of the combined beam.

Tables (1)

Tables Icon

Table 1. Normalized Average Metrics at Different Stages in Different Turbulence